Saturday, September 21, 2013

Is the wavefunction ontological or epistemological?

What is wrong with GRW and MWI?

In this post I’ll present the problems encountered by two
interpretations, GRW and the many-worlds interpretation (MWI).

In GRW theory,
the wavefunction spontaneously collapses from time to time and this solves the
measurement problem. However, GRW is a departure from quantum mechanics and the
loss of unitarity leads to the universe heating up – a prediction which can be
ultimately confirmed or rejected experimentally. The free parameters of the
theory are tuned (picked) in such a way that currently we cannot measure this
effect, but this does not rule out future more sensitive experiments. So GRW is
technically not quantum mechanics and not an interpretation. My dislike of GRW
stems from the fact that it is a stochastic theory and stochastic theories are not
theories of nature since they violate the Hamiltonian or Lagrangean formalism.
But ultimately experiments will decide the fate of GRW.

The Many-Worlds interpretation is a genuine interpretation of quantum mechanics and its aim is to solve the
measurement problem while rejecting the collapse postulate and preserving full
unitary time evolution. The basic idea is this: upon measurement, the
wavefunction splits into two parts, and each part lives into a different
universe.

You may say this is preposterous because there should be zillions
of universes and we witness only one. However, those universes are not
interacting with one another so from your point of view, everything looks
like the universe we experience every day.

Late Sidney Coleman once presented the following dialog:

-Why did people once think that the Sun is going around the
Earth?

-Because it looked like that.

-But what would it look like if it were the other way
around?

So for quantum mechanics:

-Why does the wavefunction collapse during measurement?

-Because it looks like that.

-What would it look like if there were no collapse?

Now if MWI is actually true, it would mean several things.
For one, we will all be immortals (although the fraction of universes for which
we continue to live in would be so tiny that it would not occur in practice).
Also, it will affect the reasoning of a rational person playing Russian roulette.

But there is a genuine mathematical difficulty with MWI and
this was first noted by Bell
himself. OK, the world splits, but HOW? There
are many ways a wavefunction can be decomposed. In other words, the decomposition is not unique and the question becomes why is there a preferred basis for decomposition? Currently MWI gets its
support from decoherence which specifies a preferred basis. But this is ad-hoc. Why is a particular time evolution (decoherence) singled out in this process? There is tension between the two stories: decoherence convinces us that it is very natural to not observe superposition because it is a consequence of an unremarkable and mundane time evolution, while MWI distinguishes and singles out the end state. Something is fishy in this story.

I fully agree
with Zurek that MWI has the feeling of a cheap shot in solving the measurement
problem. The story is therefore more complex and we need to be looking for an
explanation within quantum mechanics itself. The spirit of MWI lives on but the
first cut at solving the measurement problem is not good enough.

For me from all current interpretations, the one I like the
most are the positions of Zurek and late Asher Peres. I presented in prior
posts how I propose to change Zurek’s quantum Darwinism approach to solve the
measurement problem in a fully unitary way. There are still unresolved technical
issues, but this is a work in progress.

Next time I will present the Asher Peres/Copenhagen
interpretation and what I find objectionable there.